Graphics Reference
In-Depth Information
Chapter 3
Intensity-Based and Polarisation-Based
Approaches to Three-Dimensional Scene
Reconstruction
In contrast to triangulation-based methods, intensity-based approaches to three-
dimensional scene reconstruction (also termed 'photometric methods' by d'Angelo
and Wöhler,
2008
), exploit the pixel grey values in the image to recover the shape
of a surface or an object. Shadows in multiple images of a surface acquired under
different illumination conditions may contain a significant amount of information
about the surface shape (shape from shadow, cf. Sect.
3.1
). The pixel grey values
can be used to determine the position-dependent surface orientation, which by inte-
gration yields a depth map of the surface (shape from shading, cf. Sect.
3.2
). Making
use of the intensity information contained in multiple images leads to the photomet-
ric stereo approach described in Sect.
3.3
. Utilising polarisation information of the
reflected light instead of its intensity under certain circumstances allows a more
accurate determination of surface orientation (shape from polarisation, Sect.
3.4
).
3.1 Shape from Shadow
A shadow in the image of a surface contains information about the depth differ-
ence on the surface between the starting point of the shadow, e.g. the summit of a
mountain, and its end point situated downslope and corresponding to the shadow
tip, given that the direction of incident light is known. Determination of a height
difference
Δz
by determination of the shadow length
l
relies on the relation
Δz
=
l
tan
μ,
(3.1)
where
μ
is the elevation angle of the light source and
l
has to be measured along
the azimuthal direction of the incident light. Here, the geometric information
l
is
extracted by regarding photometric information, in this case the absence of light in
certain parts of the image of the surface. Hence, shadow information can commonly
be obtained from an image by a thresholding operation.
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